Akademik Veri Yönetim Sistemi
Georgian Mathematical Journal, 2023 (SCI-Expanded)
Let φ i {\Phi{i}} be Young functions and ω i {\omega{i}} be weights on d {\mathbb{R}{d}}, i = 1, 2, 3 {i=1,2,3}. A locally integrable function m (ζ, η) {m(\xi,\eta)} on d × d {\mathbb{R}{d}\times\mathbb{R}{d}} is said to be a bilinear multiplier on d {\mathbb{R}{d}} of type (φ 1, ω 1; φ 2, ω 2; φ 3, ω 3) {(\Phi{1},\omega{1};\Phi{2},\omega{2};\Phi{3},\omega{3})} if B m (f 1, f 2) (x) = 1 (ζ) f 2 (η) m (ζ, η) e 2 π i 〈 ζ + η, x ζ η B{m}(f{1},f{2})(x)=\int{\mathbb{R}{d}}\int{\mathbb{R}{d}}\hat{f{1}}(% \xi)\hat{f{2}}(\eta)m(\xi,\eta)e{2\pi i\langle\xi+\eta,x\rangle}\,d\xi\,d\eta defines a bounded bilinear operator from L ω 1 φ 1 (d) × L ω 2 φ 2 (d) {L{\Phi{1}}{\omega{1}}(\mathbb{R}{d})\times L{\Phi{2}}{\omega{2}}(% \mathbb{R}{d})} to L ω 3 φ 3 (d) {L{\Phi{3}}{\omega{3}}(\mathbb{R}{d})}. We deduce some properties of this class of operators. Moreover, we give the methods to generate bilinear multipliers between weighted Orlicz spaces.